Question

A particle of mass 0.5 g and charge 10 \(\mu\)C is subjected to a uniform electric field of 8 NC\(^{-1}\). If the particle is initially at rest, the velocity of the particle after a time of 5 seconds is

• A. \( 5 \) ms\(^{-1} \)
• B. \( 0.5 \) ms\(^{-1} \)
• C. \( 8 \) ms\(^{-1} \)
• D. \( 0.8 \) ms\(^{-1} \)

Hint:

Remember the formula for force on a charge in an electric field and the equations of motion.

Answer 1

The Correct Option is D

Given: Mass of the particle, \( m = 0.5 \) g = \( 0.5 \times 10^{-3} \) kg Charge of the particle, \( q = 10 \mu \)C = \( 10 \times 10^{-6} \) C Electric field, \( E = 8 \) NC\(^{-1} \) Initial velocity, \( u = 0 \) ms\(^{-1} \) Time, \( t = 5 \) s The force experienced by the particle in the electric field is given by \[ F = qE \] \[ F = 10 \times 10^{-6} \times 8 = 80 \times 10^{-6} \text{ N} \] The acceleration of the particle is given by \[ a = \frac{F}{m} \] \[ a = \frac{80 \times 10^{-6}}{0.5 \times 10^{-3}} = \frac{80}{0.5} \times 10^{-3} = 160 \times 10^{-3} = 0.16 \text{ ms}^{-2} \] Using the equation of motion, \( v = u + at \), we have \[ v = 0 + 0.16 \times 5 \] \[ v = 0.8 \text{ ms}^{-1} \] Therefore, the velocity of the particle after 5 seconds is \( 0.8 \) ms\(^{-1} \).